Not quite sure what you mean by forms, do you just mean examples of?
If so Greek sports such as wrestling and discus throwing were particularly popular, as well as atheletic events such as distance running and sprinting. There was also a running event that became popular for a period of time that was done in full military armour.
Greek drama tended to focus on tragedy, think Aeschylus, Euripides and Sophocles. Another genre would be comedy, which although popular, was mostly considered inferior to tragedy (at the time- according to Aristotle at least). Think Aristophanes for examples of comedy. Those two are the main genres of Greek drama.
Greek entertainment mostly considered of sports and drama, but other things that the ancient Greeks (well, the wealthy ones) enjoyed doing were partying- including listening to music, drinking, symposiums (philosophical discussions). In addition, working out was a big part of the young wealthy aristocrats lifestyle, visiting the gymnasium was a staple activity among the aristocracy, especially in the fifth and four centuries BC. Again remember that these activities were mostly done by the rich who could afford to not work all the time.
Hope that helped, sorry it was brief as I have to shoot and sorry if I misunderstood the question.